On the problem to construct the minimum circle enclosing n given points in a plane

Abstract

If we consider the circle circumscribing any triangle ABC (see figures 11, 12), and diminish its radius still causing it to pass through A and B: then if ACB be an acute angle, C passes without the circle, but if ACB be an obtuse angle, C remains within the circle. If C be a right angle, the radius of the circle, being ½AB, cannot be farther diminished.